[Proof of Theorem  REF.] Note that under the assumptions of Theorem REF , (A.12) and Lemma REF  hold. Thus, as an analogy to the proof of Theorem 4.4 in [1]}, it suffices to show that
\(\frac{\int _{||\Delta _{\mathcal {Z}}||_{\operatorname{F}}\le \eta _n}\exp \left(-\frac{n}{2}\left(\frac{1}{2}\tilde{\Delta }_{\mathcal {Z}}^t\operatorname{H}_{\Sigma _{\mathcal {Z}}^*}\tilde{\Delta }_{\mathcal {Z}}+R_n\right)\right)d\Delta _{\mathcal {Z}}}{\int _{||\Delta _{\mathcal {Z}}||_{\operatorname{F}}\le \eta _n} \exp \left(-\frac{n}{4}\tilde{\Delta }_{\mathcal {Z}}^t\operatorname{H}_{\Sigma _{\mathcal {Z}}^*}\tilde{\Delta }_{\mathcal {Z}}\right)d\Delta _{\mathcal {Z}}}\rightarrow 1\) 
